Small concepts with enormous implications

The software field — really, any scientific field — tends to advance most quickly and impressively on those few occasions when someone (i.e., not a committee) comes up with an idea that is small in concept yet enormous in its implications.

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9 thoughts on “Small concepts with enormous implications”

What would the cumulative distribution of scientists’ contributions to science look like? If you somehow ranked the N currently active scientist, from least contributing to most, and plotted n/N vs the sum of the contributions from scientists 1 through n, what would you get?

It would be interesting to know if, say, the top 5% of scientists contribute 50% or more of the science, etc. What fields are more concentrated at the top? Which are more evenly spread out?

What is the Gini coefficient of economists? I seem to recall seeing a rating system for all economists, based on citations of their papers. Perhaps someone has already done such an analysis.

Assessing contributions, yes, a tough question. How many digits of precision of how many elements do you need to determine before your contribution is equal to Mendeleev’s? That’s (nearly) a ridiculous question.

What if it has something to do with how much a scientist’s work opens new avenues of enquiry? Sounds promising, but by this definition, if a scientist single-handedly created and answered most of the open questions in a field—thinking of Claude Shannon and information theory—then this definition would minimize that scientist’s contribution.

Then perhaps it’s how applicable a scientist’s work is to other fields. (Shannon does much better under this model.) Or perhaps it’s about contribution to the outside world, whether of practical engineering or to the wider society.

John V., I think that’s something that might be useful, but consider how many people have cited Newton recently. And science is something that is more than a bunch of activities that exist only toward the end of publishing papers—and being cited—though that’s what science perhaps often looks like today.

Google’s original PageRank paper is obsolete: these days Google and other search engines consider many signals when determining a page’s worth. And PageRank is ultimately about finding the best page for a given query, not the Best Page Ever.

All of these formulæ are awesome but I think—and I hope we all can agree on this—that questions like this come down to judgement, and each person’s answer says as much about the person providing the answer as it does about the people who we individually argue for.

I’m ultimately not going to begrudge anyone the opinion that Copernicus or Galileo Newton or Leibnitz or or Einstein or even Feynman for that matter is the Best Scientist Ever. A compelling story is going to trump the facts, because this is not about counting protons, it’s about what we find admirable and inspiring and important.

That makes a lot of sense, especially considering past scientists. For some reason I was thinking about judging today’s scientists, but of course many tremendous scientists were from years past. Just the fact that we know who they are and what they contributed shows that their contributions were important.

I had a professor in grad school who considered Aristotle the greatest, because of his emphasis on empiricism — although these days he would probably not be classified as a scientist.

A related idea I often think about is how rare it is that someone like Newton or Einstein appears. If you think of people who are ‘one in a million’, these days there are almost 7,000 such people in the world. When Einstein flourished there would have been fewer than 2,000 such individuals, and a large proportion of them would probably have been unknown to the European community. Or from the other perspective, we might expect that there are four Einsteins around today. Condidering the size of the scientific community in Newton’s time, we might expect that there are many Newtons around.

Of course the nature of the times and the state of the art have a fundamental influence on what such people might contribute, so there is every reason to think that Newton or Einstein flourishing today mignt not even be recognized, but I think it is interesting to wonder about.

Regarding Feynman, I am not competent to judge his scientific contributions but I feel strongly that he is famous primarily due to his personality and the stories people tell about him. I agree completely that a compelling story will trump the facts.

John: The Medici Effect makes a similar argument, though looking at da Vinci rather than Newton. There should be thousands of people in the world now that have da Vinci’s inborn talent. But the author argues that it takes more than genetic endowment to create a da Vinci: it also takes a Renaissance Florence.

Per my earlier post, I wonder how much time our modern-day Newton’s are spending chasing grants. We could use more modern-day Medicis to free more creative individuals from the distraction of grantmongering.

Yes, grantmongering and being stuck in traffic on their daily commute!

Everyone knows about the MacArthur Foundation, but I recently met a gentleman who is supporting theological scholarship, Mark Lanier. His theological library seems very nice (although I’m not qualified to judge the contents) and he sponsors talks by various people at the library. It is all free to the public and from what I can tell entirely supported by him. I attended a lecture there on the Dead Sea Scrolls recently and it was very interesting. While I was at the talk the old-time patrons of scholars came to mind.

I heard someone from the MacArthur Foundation say that it is surprisingly difficult for them to contact winners of their genius awards. By the time someone gains the attention of the Foundation, they’re not simply working in a lab in obscurity. They’re busy executives. You typically have to have gotten a lot of other grant funding first to be famous enough to attract a MacArthur grant. One would hope that a MacArthur grant would free some people to go back to doing what made them famous.